Problem: Solve for $x$ and $y$ using substitution. ${2x+5y = -9}$ ${x = -4y-12}$
Answer: Since $x$ has already been solved for, substitute $-4y-12$ for $x$ in the first equation. ${2}{(-4y-12)}{+ 5y = -9}$ Simplify and solve for $y$ $-8y-24 + 5y = -9$ $-3y-24 = -9$ $-3y-24{+24} = -9{+24}$ $-3y = 15$ $\dfrac{-3y}{{-3}} = \dfrac{15}{{-3}}$ ${y = -5}$ Now that you know ${y = -5}$ , plug it back into $\thinspace {x = -4y-12}\thinspace$ to find $x$ ${x = -4}{(-5)}{ - 12}$ $x = 20 - 12$ ${x = 8}$ You can also plug ${y = -5}$ into $\thinspace {2x+5y = -9}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(-5)}{= -9}$ ${x = 8}$